# Difference of two large numbers

Given two numbers as strings. The numbers may be very large (may not fit in long long int), the task is to find the difference between these two numbers.

Examples:

```Input : str1 = "11443333311111111100",
str2 =     "1144422222221111"
Output : 11442188888888889989

Input :str1 = "122387876566565674",
str2 =     "31435454654554"
Output : 122356441111911120```
Recommended Practice

This is simply based on school mathematics. We traverse both strings from the end, one by one subtract digits.

1. Reverse both strings.
2. Keep subtracting digits one by one from 0â€™th index (in reversed strings) to the end of a smaller string, append the diff if it’s positive to end of the result. If difference(diff) is negative then add 10 and keep track of carry as 1 if it’s positive then carry is 0.
3. Finally, reverse the result.

Below is the implementation of the above idea:

## C++

 `// C++ program to find difference of two large numbers. ` `#include ` `using` `namespace` `std; ` ` `  `// Returns true if str1 is smaller than str2. ` `bool` `isSmaller(string str1, string str2) ` `{ ` `    ``// Calculate lengths of both string ` `    ``int` `n1 = str1.length(), n2 = str2.length(); ` ` `  `    ``if` `(n1 < n2) ` `        ``return` `true``; ` `    ``if` `(n2 < n1) ` `        ``return` `false``; ` ` `  `    ``for` `(``int` `i = 0; i < n1; i++) ` `        ``if` `(str1[i] < str2[i]) ` `            ``return` `true``; ` `        ``else` `if` `(str1[i] > str2[i]) ` `            ``return` `false``; ` ` `  `    ``return` `false``; ` `} ` ` `  `// Function for find difference of larger numbers ` `string findDiff(string str1, string str2) ` `{ ` `    ``// Before proceeding further, make sure str1 ` `    ``// is not smaller ` `    ``if` `(isSmaller(str1, str2)) ` `        ``swap(str1, str2); ` ` `  `    ``// Take an empty string for storing result ` `    ``string str = ``""``; ` ` `  `    ``// Calculate length of both string ` `    ``int` `n1 = str1.length(), n2 = str2.length(); ` ` `  `    ``// Reverse both of strings ` `    ``reverse(str1.begin(), str1.end()); ` `    ``reverse(str2.begin(), str2.end()); ` ` `  `    ``int` `carry = 0; ` ` `  `    ``// Run loop till small string length ` `    ``// and subtract digit of str1 to str2 ` `    ``for` `(``int` `i = 0; i < n2; i++) { ` `        ``// Do school mathematics, compute difference of ` `        ``// current digits ` ` `  `        ``int` `sub ` `            ``= ((str1[i] - ``'0'``) - (str2[i] - ``'0'``) - carry); ` ` `  `        ``// If subtraction is less than zero ` `        ``// we add then we add 10 into sub and ` `        ``// take carry as 1 for calculating next step ` `        ``if` `(sub < 0) { ` `            ``sub = sub + 10; ` `            ``carry = 1; ` `        ``} ` `        ``else` `            ``carry = 0; ` ` `  `        ``str.push_back(sub + ``'0'``); ` `    ``} ` ` `  `    ``// subtract remaining digits of larger number ` `    ``for` `(``int` `i = n2; i < n1; i++) { ` `        ``int` `sub = ((str1[i] - ``'0'``) - carry); ` ` `  `        ``// if the sub value is -ve, then make it positive ` `        ``if` `(sub < 0) { ` `            ``sub = sub + 10; ` `            ``carry = 1; ` `        ``} ` `        ``else` `            ``carry = 0; ` ` `  `        ``str.push_back(sub + ``'0'``); ` `    ``} ` ` `  `    ``// reverse resultant string ` `    ``reverse(str.begin(), str.end()); ` ` `  `    ``return` `str; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string str1 = ``"978"``; ` `    ``string str2 = ``"12977"``; ` ` `  `    ``// Function call ` `    ``cout << findDiff(str1, str2) << endl; ` ` `  `    ``string s1 = ``"100"``; ` `    ``string s2 = ``"1000000"``; ` `   `  `    ``// Function call ` `    ``cout << findDiff(s1, s2); ` ` `  `    ``return` `0; ` `}`

## Java

 `// Java program to find difference of two large numbers. ` `import` `java.util.*; ` ` `  `class` `GFG { ` ` `  `    ``// Returns true if str1 is smaller than str2. ` `    ``static` `boolean` `isSmaller(String str1, String str2) ` `    ``{ ` `        ``// Calculate lengths of both string ` `        ``int` `n1 = str1.length(), n2 = str2.length(); ` `        ``if` `(n1 < n2) ` `            ``return` `true``; ` `        ``if` `(n2 < n1) ` `            ``return` `false``; ` ` `  `        ``for` `(``int` `i = ``0``; i < n1; i++) ` `            ``if` `(str1.charAt(i) < str2.charAt(i)) ` `                ``return` `true``; ` `            ``else` `if` `(str1.charAt(i) > str2.charAt(i)) ` `                ``return` `false``; ` ` `  `        ``return` `false``; ` `    ``} ` ` `  `    ``// Function for find difference of larger numbers ` `    ``static` `String findDiff(String str1, String str2) ` `    ``{ ` `        ``// Before proceeding further, make sure str1 ` `        ``// is not smaller ` `        ``if` `(isSmaller(str1, str2)) { ` `            ``String t = str1; ` `            ``str1 = str2; ` `            ``str2 = t; ` `        ``} ` ` `  `        ``// Take an empty string for storing result ` `        ``String str = ``""``; ` ` `  `        ``// Calculate length of both string ` `        ``int` `n1 = str1.length(), n2 = str2.length(); ` ` `  `        ``// Reverse both of strings ` `        ``str1 = ``new` `StringBuilder(str1).reverse().toString(); ` `        ``str2 = ``new` `StringBuilder(str2).reverse().toString(); ` ` `  `        ``int` `carry = ``0``; ` ` `  `        ``// Run loop till small string length ` `        ``// and subtract digit of str1 to str2 ` `        ``for` `(``int` `i = ``0``; i < n2; i++) { ` `            ``// Do school mathematics, compute difference of ` `            ``// current digits ` `            ``int` `sub ` `                ``= ((``int``)(str1.charAt(i) - ``'0'``) ` `                   ``- (``int``)(str2.charAt(i) - ``'0'``) - carry); ` ` `  `            ``// If subtraction is less than zero ` `            ``// we add then we add 10 into sub and ` `            ``// take carry as 1 for calculating next step ` `            ``if` `(sub < ``0``) { ` `                ``sub = sub + ``10``; ` `                ``carry = ``1``; ` `            ``} ` `            ``else` `                ``carry = ``0``; ` ` `  `            ``str += (``char``)(sub + ``'0'``); ` `        ``} ` ` `  `        ``// subtract remaining digits of larger number ` `        ``for` `(``int` `i = n2; i < n1; i++) { ` `            ``int` `sub = ((``int``)(str1.charAt(i) - ``'0'``) - carry); ` ` `  `            ``// if the sub value is -ve, then make it ` `            ``// positive ` `            ``if` `(sub < ``0``) { ` `                ``sub = sub + ``10``; ` `                ``carry = ``1``; ` `            ``} ` `            ``else` `                ``carry = ``0``; ` ` `  `            ``str += (``char``)(sub + ``'0'``); ` `        ``} ` ` `  `        ``// reverse resultant string ` `        ``return` `new` `StringBuilder(str).reverse().toString(); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``String str1 = ``"978"``; ` `        ``String str2 = ``"12977"``; ` ` `  `        ``// Function call ` `        ``System.out.println(findDiff(str1, str2)); ` ` `  `        ``String s1 = ``"100"``; ` `        ``String s2 = ``"1000000"``; ` `       `  `        ``// Function call ` `        ``System.out.println(findDiff(s1, s2)); ` `    ``} ` `} ` ` `  `// This code is contributed by mits`

## Python3

 `# Python 3 program to find difference of two large numbers. ` ` `  `# Returns true if str1 is smaller than str2. ` ` `  ` `  `def` `isSmaller(str1, str2): ` ` `  `    ``# Calculate lengths of both string ` `    ``n1 ``=` `len``(str1) ` `    ``n2 ``=` `len``(str2) ` ` `  `    ``if` `(n1 < n2): ` `        ``return` `True` `    ``if` `(n2 < n1): ` `        ``return` `False` ` `  `    ``for` `i ``in` `range``(n1): ` `        ``if` `(str1[i] < str2[i]): ` `            ``return` `True` `        ``elif` `(str1[i] > str2[i]): ` `            ``return` `False` ` `  `    ``return` `False` ` `  `# Function for find difference of larger numbers ` ` `  ` `  `def` `findDiff(str1, str2): ` ` `  `    ``# Before proceeding further, make sure str1 ` `    ``# is not smaller ` `    ``if` `(isSmaller(str1, str2)): ` `        ``temp ``=` `str1 ` `        ``str1 ``=` `str2 ` `        ``str2 ``=` `temp ` ` `  `    ``# Take an empty string for storing result ` `    ``str3 ``=` `"" ` ` `  `    ``# Calculate length of both string ` `    ``n1 ``=` `len``(str1) ` `    ``n2 ``=` `len``(str2) ` ` `  `    ``# Reverse both of strings ` `    ``str1 ``=` `str1[::``-``1``] ` `    ``str2 ``=` `str2[::``-``1``] ` ` `  `    ``carry ``=` `0` ` `  `    ``# Run loop till small string length ` `    ``# and subtract digit of str1 to str2 ` `    ``for` `i ``in` `range``(n2): ` ` `  `        ``# Do school mathematics, compute difference of ` `        ``# current digits ` ` `  `        ``sub ``=` `((``ord``(str1[i])``-``ord``(``'0'``))``-``(``ord``(str2[i])``-``ord``(``'0'``))``-``carry) ` ` `  `        ``# If subtraction is less than zero ` `        ``# we add then we add 10 into sub and ` `        ``# take carry as 1 for calculating next step ` `        ``if` `(sub < ``0``): ` ` `  `            ``sub ``=` `sub ``+` `10` `            ``carry ``=` `1` ` `  `        ``else``: ` `            ``carry ``=` `0` ` `  `        ``str3 ``=` `str3``+``str``(sub) ` ` `  `    ``# subtract remaining digits of larger number ` `    ``for` `i ``in` `range``(n2, n1): ` ` `  `        ``sub ``=` `((``ord``(str1[i])``-``ord``(``'0'``)) ``-` `carry) ` ` `  `        ``# if the sub value is -ve, then make it positive ` `        ``if` `(sub < ``0``): ` ` `  `            ``sub ``=` `sub ``+` `10` `            ``carry ``=` `1` ` `  `        ``else``: ` `            ``carry ``=` `0` ` `  `        ``str3 ``=` `str3``+``str``(sub) ` ` `  `    ``# reverse resultant string ` `    ``str3 ``=` `str3[::``-``1``] ` ` `  `    ``return` `str3 ` ` `  ` `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``str1 ``=` `"978"` `    ``str2 ``=` `"12977"` `     `  `    ``# Function call ` `    ``print``(findDiff(str1, str2)) ` ` `  `    ``s1 ``=` `"100"` `    ``s2 ``=` `"1000000"` `     `  `    ``# Function call ` `    ``print``(findDiff(s1, s2)) ` ` `  `# This code is contributed by ChitraNayal `

## C#

 `// C# program to find difference of two large numbers. ` `using` `System; ` `using` `System.Collections; ` ` `  `class` `GFG { ` ` `  `    ``// Returns true if str1 is smaller than str2. ` `    ``static` `bool` `isSmaller(``string` `str1, ``string` `str2) ` `    ``{ ` `        ``// Calculate lengths of both string ` `        ``int` `n1 = str1.Length, n2 = str2.Length; ` `        ``if` `(n1 < n2) ` `            ``return` `true``; ` `        ``if` `(n2 < n1) ` `            ``return` `false``; ` ` `  `        ``for` `(``int` `i = 0; i < n1; i++) ` `            ``if` `(str1[i] < str2[i]) ` `                ``return` `true``; ` `            ``else` `if` `(str1[i] > str2[i]) ` `                ``return` `false``; ` ` `  `        ``return` `false``; ` `    ``} ` ` `  `    ``// Function for find difference of larger numbers ` `    ``static` `string` `findDiff(``string` `str1, ``string` `str2) ` `    ``{ ` `        ``// Before proceeding further, make sure str1 ` `        ``// is not smaller ` `        ``if` `(isSmaller(str1, str2)) { ` `            ``string` `t = str1; ` `            ``str1 = str2; ` `            ``str2 = t; ` `        ``} ` ` `  `        ``// Take an empty string for storing result ` `        ``string` `str = ``""``; ` ` `  `        ``// Calculate length of both string ` `        ``int` `n1 = str1.Length, n2 = str2.Length; ` ` `  `        ``// Reverse both of strings ` `        ``char``[] ch1 = str1.ToCharArray(); ` `        ``Array.Reverse(ch1); ` `        ``str1 = ``new` `string``(ch1); ` `        ``char``[] ch2 = str2.ToCharArray(); ` `        ``Array.Reverse(ch2); ` `        ``str2 = ``new` `string``(ch2); ` ` `  `        ``int` `carry = 0; ` ` `  `        ``// Run loop till small string length ` `        ``// and subtract digit of str1 to str2 ` `        ``for` `(``int` `i = 0; i < n2; i++) { ` `            ``// Do school mathematics, compute difference of ` `            ``// current digits ` `            ``int` `sub = ((``int``)(str1[i] - ``'0'``) ` `                       ``- (``int``)(str2[i] - ``'0'``) - carry); ` ` `  `            ``// If subtraction is less than zero ` `            ``// we add then we add 10 into sub and ` `            ``// take carry as 1 for calculating next step ` `            ``if` `(sub < 0) { ` `                ``sub = sub + 10; ` `                ``carry = 1; ` `            ``} ` `            ``else` `                ``carry = 0; ` ` `  `            ``str += (``char``)(sub + ``'0'``); ` `        ``} ` ` `  `        ``// subtract remaining digits of larger number ` `        ``for` `(``int` `i = n2; i < n1; i++) { ` `            ``int` `sub = ((``int``)(str1[i] - ``'0'``) - carry); ` ` `  `            ``// if the sub value is -ve, then make it ` `            ``// positive ` `            ``if` `(sub < 0) { ` `                ``sub = sub + 10; ` `                ``carry = 1; ` `            ``} ` `            ``else` `                ``carry = 0; ` ` `  `            ``str += (``char``)(sub + ``'0'``); ` `        ``} ` ` `  `        ``// reverse resultant string ` `        ``char``[] ch3 = str.ToCharArray(); ` `        ``Array.Reverse(ch3); ` `        ``return` `new` `string``(ch3); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``string` `str1 = ``"978"``; ` `        ``string` `str2 = ``"12977"``; ` ` `  `        ``// Function call ` `        ``Console.WriteLine(findDiff(str1, str2)); ` ` `  `        ``string` `s1 = ``"100"``; ` `        ``string` `s2 = ``"1000000"``; ` `       `  `        ``// Function call  ` `        ``Console.WriteLine(findDiff(s1, s2)); ` `    ``} ` `} ` ` `  `// This code is contributed by mits`

## PHP

 ` ``\$str2``[``\$i``]) ` `        ``return` `false; ` ` `  `    ``return` `false; ` `} ` ` `  `// Function for find difference of larger numbers ` `function` `findDiff(``\$str1``, ``\$str2``) ` `{ ` `    ``// Before proceeding further, make sure str1 ` `    ``// is not smaller ` `    ``if` `(isSmaller(``\$str1``, ``\$str2``)){ ` `        ``\$t``=``\$str1``; ` `        ``\$str1``=``\$str2``; ` `        ``\$str2``=``\$t``; ` `    ``} ` ` `  `    ``// Take an empty string for storing result ` `    ``\$str` `= ``""``; ` ` `  `    ``// Calculate length of both string ` `    ``\$n1` `= ``strlen``(``\$str1``); ` `    ``\$n2` `= ``strlen``(``\$str2``); ` ` `  `    ``// Reverse both of strings ` `    ``\$str1``=``strrev``(``\$str1``); ` `    ``\$str2``=``strrev``(``\$str2``); ` `     `  `    ``\$carry` `= 0; ` ` `  `    ``// Run loop till small string length ` `    ``// and subtract digit of str1 to str2 ` `    ``for` `(``\$i``=0; ``\$i``<``\$n2``; ``\$i``++) ` `    ``{ ` `        ``// Do school mathematics, compute difference of ` `        ``// current digits ` `         `  `        ``\$sub``=((ord(``\$str1``[``\$i``])-ord(``'0'``))-(ord(``\$str2``[``\$i``])-ord(``'0'``))-``\$carry``); ` `         `  `        ``// If subtraction is less than zero ` `        ``// we add then we add 10 into sub and ` `        ``// take carry as 1 for calculating next step ` `        ``if` `(``\$sub` `< 0) ` `        ``{ ` `            ``\$sub` `= ``\$sub` `+ 10; ` `            ``\$carry` `= 1; ` `        ``} ` `        ``else` `            ``\$carry` `= 0; ` ` `  `        ``\$str``.=``chr``(``\$sub``+48); ` `    ``} ` ` `  `    ``// subtract remaining digits of larger number ` `    ``for` `(``\$i``=``\$n2``; ``\$i``<``\$n1``; ``\$i``++) ` `    ``{ ` `        ``\$sub` `= ((ord(``\$str1``[``\$i``])-ord(``'0'``)) - ``\$carry``); ` `         `  `        ``// if the sub value is -ve, then make it positive ` `        ``if` `(``\$sub` `< 0) ` `        ``{ ` `            ``\$sub` `= ``\$sub` `+ 10; ` `            ``\$carry` `= 1; ` `        ``} ` `        ``else` `            ``\$carry` `= 0; ` `             `  `        ``\$str``.=``chr``(``\$sub``+48); ` `    ``} ` ` `  `    ``// reverse resultant string ` `    ``\$str``=``strrev``(``\$str``); ` ` `  `    ``return` `\$str``; ` `} ` ` `  `// Driver code ` ` `  `    ``\$str1` `= ``"978"``; ` `    ``\$str2` `= ``"12977"``; ` ` `  `    ``// Function call  ` `    ``echo` `findDiff(``\$str1``, ``\$str2``).``"\n"``; ` `     `  `    ``\$s1` `= ``"100"``; ` `    ``\$s2` `= ``"1000000"``; ` ` `  `    ``// Function call  ` `    ``echo` `findDiff(``\$s1``,``\$s2``); ` `     `  `// This code is contributed by mits ` `?> `

## Javascript

 ` `

Output

```11999
0999900```

Time Complexity: O(n1 + n2)

Auxiliary Space: O(max(n1, n2))
Optimized solution :
We can avoid the first two string reverse operations by traversing them from the end.

Below is the optimized solution.

## C++

 `// C++ program to find difference of two large numbers. ` `#include ` `using` `namespace` `std; ` ` `  `// Returns true if str1 is smaller than str2, ` `// else false. ` `bool` `isSmaller(string str1, string str2) ` `{ ` `    ``// Calculate lengths of both string ` `    ``int` `n1 = str1.length(), n2 = str2.length(); ` ` `  `    ``if` `(n1 < n2) ` `        ``return` `true``; ` `    ``if` `(n2 < n1) ` `        ``return` `false``; ` ` `  `    ``for` `(``int` `i = 0; i < n1; i++) { ` `        ``if` `(str1[i] < str2[i]) ` `            ``return` `true``; ` `        ``else` `if` `(str1[i] > str2[i]) ` `            ``return` `false``; ` `    ``} ` `    ``return` `false``; ` `} ` ` `  `// Function for finding difference of larger numbers ` `string findDiff(string str1, string str2) ` `{ ` `    ``// Before proceeding further, make sure str1 ` `    ``// is not smaller ` `    ``if` `(isSmaller(str1, str2)) ` `        ``swap(str1, str2); ` ` `  `    ``// Take an empty string for storing result ` `    ``string str = ``""``; ` ` `  `    ``// Calculate lengths of both string ` `    ``int` `n1 = str1.length(), n2 = str2.length(); ` `    ``int` `diff = n1 - n2; ` ` `  `    ``// Initially take carry zero ` `    ``int` `carry = 0; ` ` `  `    ``// Traverse from end of both strings ` `    ``for` `(``int` `i = n2 - 1; i >= 0; i--) { ` `        ``// Do school mathematics, compute difference of ` `        ``// current digits and carry ` `        ``int` `sub = ((str1[i + diff] - ``'0'``) - (str2[i] - ``'0'``) ` `                   ``- carry); ` `        ``if` `(sub < 0) { ` `            ``sub = sub + 10; ` `            ``carry = 1; ` `        ``} ` `        ``else` `            ``carry = 0; ` ` `  `        ``str.push_back(sub + ``'0'``); ` `    ``} ` ` `  `    ``// subtract remaining digits of str1[] ` `    ``for` `(``int` `i = n1 - n2 - 1; i >= 0; i--) { ` `        ``if` `(str1[i] == ``'0'` `&& carry) { ` `            ``str.push_back(``'9'``); ` `            ``continue``; ` `        ``} ` `        ``int` `sub = ((str1[i] - ``'0'``) - carry); ` `        ``if` `(i > 0 || sub > 0) ``// remove preceding 0's ` `            ``str.push_back(sub + ``'0'``); ` `        ``carry = 0; ` `    ``} ` ` `  `    ``// reverse resultant string ` `    ``reverse(str.begin(), str.end()); ` ` `  `    ``return` `str; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string str1 = ``"88"``; ` `    ``string str2 = ``"1079"``; ` `   `  `    ``// Function call ` `    ``cout << findDiff(str1, str2); ` `    ``return` `0; ` `}`

## Java

 `// Java program to find difference of two large numbers. ` ` `  `class` `GFG { ` ` `  `    ``// Returns true if str1 is smaller than str2, ` `    ``// else false. ` `    ``static` `boolean` `isSmaller(String str1, String str2) ` `    ``{ ` `        ``// Calculate lengths of both string ` `        ``int` `n1 = str1.length(), n2 = str2.length(); ` ` `  `        ``if` `(n1 < n2) ` `            ``return` `true``; ` `        ``if` `(n2 < n1) ` `            ``return` `false``; ` ` `  `        ``for` `(``int` `i = ``0``; i < n1; i++) { ` `            ``if` `(str1.charAt(i) < str2.charAt(i)) ` `                ``return` `true``; ` `            ``else` `if` `(str1.charAt(i) > str2.charAt(i)) ` `                ``return` `false``; ` `        ``} ` `        ``return` `false``; ` `    ``} ` ` `  `    ``// Function for finding difference of larger numbers ` `    ``static` `String findDiff(String str1, String str2) ` `    ``{ ` `        ``// Before proceeding further, make sure str1 ` `        ``// is not smaller ` `        ``if` `(isSmaller(str1, str2)) { ` `            ``String t = str1; ` `            ``str1 = str2; ` `            ``str2 = t; ` `        ``} ` ` `  `        ``// Take an empty string for storing result ` `        ``String str = ``""``; ` ` `  `        ``// Calculate lengths of both string ` `        ``int` `n1 = str1.length(), n2 = str2.length(); ` `        ``int` `diff = n1 - n2; ` ` `  `        ``// Initially take carry zero ` `        ``int` `carry = ``0``; ` ` `  `        ``// Traverse from end of both strings ` `        ``for` `(``int` `i = n2 - ``1``; i >= ``0``; i--) { ` `            ``// Do school mathematics, compute difference of ` `            ``// current digits and carry ` `            ``int` `sub ` `                ``= (((``int``)str1.charAt(i + diff) - (``int``)``'0'``) ` `                   ``- ((``int``)str2.charAt(i) - (``int``)``'0'``) ` `                   ``- carry); ` `            ``if` `(sub < ``0``) { ` `                ``sub = sub + ``10``; ` `                ``carry = ``1``; ` `            ``} ` `            ``else` `                ``carry = ``0``; ` ` `  `            ``str += String.valueOf(sub); ` `        ``} ` ` `  `        ``// subtract remaining digits of str1[] ` `        ``for` `(``int` `i = n1 - n2 - ``1``; i >= ``0``; i--) { ` `            ``if` `(str1.charAt(i) == ``'0'` `&& carry > ``0``) { ` `                ``str += ``"9"``; ` `                ``continue``; ` `            ``} ` `            ``int` `sub = (((``int``)str1.charAt(i) - (``int``)``'0'``) ` `                       ``- carry); ` `            ``if` `(i > ``0` `|| sub > ``0``) ``// remove preceding 0's ` `                ``str += String.valueOf(sub); ` `            ``carry = ``0``; ` `        ``} ` ` `  `        ``// reverse resultant string ` `        ``return` `new` `StringBuilder(str).reverse().toString(); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``String str1 = ``"88"``; ` `        ``String str2 = ``"1079"``; ` `       `  `        ``// Function call ` `        ``System.out.println(findDiff(str1, str2)); ` `    ``} ` `} ` ` `  `// This code is contributed by mits`

## Python3

 `# Python3 program to find difference  ` `# of two large numbers. ` ` `  `# Returns true if str1 is smaller than ` `# str2, else false. ` `def` `isSmaller(str1, str2): ` `     `  `    ``# Calculate lengths of both string ` `    ``n1 ``=` `len``(str1) ` `    ``n2 ``=` `len``(str2) ` ` `  `    ``if` `(n1 < n2): ` `        ``return` `True` `    ``if` `(n2 < n1): ` `        ``return` `False` ` `  `    ``for` `i ``in` `range``(n1): ` `        ``if` `(str1[i] < str2[i]): ` `            ``return` `True` `        ``elif` `(str1[i] > str2[i]): ` `            ``return` `False` `             `  `    ``return` `False` ` `  `# Function for finding difference  ` `# of larger numbers ` `def` `findDiff(str1, str2): ` `     `  `    ``# Before proceeding further, ` `    ``# make sure str1 is not smaller ` `    ``if` `(isSmaller(str1, str2)): ` `        ``str1, str2 ``=` `str2, str1 ` ` `  `    ``# Take an empty string for ` `    ``# storing result ` `    ``Str` `=` `"" ` `     `  `    ``# Calculate lengths of both string ` `    ``n1 ``=` `len``(str1) ` `    ``n2 ``=` `len``(str2) ` `    ``diff ``=` `n1 ``-` `n2 ` `     `  `    ``# Initially take carry zero ` `    ``carry ``=` `0` `     `  `    ``# Traverse from end of both strings ` `    ``for` `i ``in` `range``(n2 ``-` `1``, ``-``1``, ``-``1``): ` `         `  `        ``# Do school mathematics, compute ` `        ``# difference of current digits ` `        ``# and carry ` `        ``sub ``=` `((``ord``(str1[i ``+` `diff]) ``-` `ord``(``'0'``)) ``-`  `               ``(``ord``(str2[i]) ``-` `ord``(``'0'``)) ``-` `carry) ` ` `  `        ``if` `(sub < ``0``): ` `            ``sub ``+``=` `10` `            ``carry ``=` `1` `        ``else``: ` `            ``carry ``=` `0` ` `  `        ``Str` `+``=` `chr``(sub ``+` `ord``(``'0'``)) ` `     `  `    ``# Subtract remaining digits of str1[] ` `    ``for` `i ``in` `range``(n1 ``-` `n2 ``-` `1``, ``-``1``, ``-``1``): ` `        ``if` `(str1[i] ``=``=` `'0'` `and` `carry): ` `            ``Str` `+``=` `'9'` `            ``continue` `             `  `        ``sub ``=` `(``ord``(str1[i]) ``-` `ord``(``'0'``)) ``-` `carry ` `         `  `        ``# Remove preceding 0's ` `        ``if` `(i > ``0` `or` `sub > ``0``):  ` `            ``Str` `+``=` `chr``(sub ``+` `ord``(``'0'``)) ` `             `  `        ``carry ``=` `0` ` `  `    ``# Reverse resultant string ` `    ``Str` `=` `Str``[::``-``1``] ` `     `  `    ``return` `Str` ` `  `# Driver code ` `str1 ``=` `"88"` `str2 ``=` `"1079"` ` `  `# Function call ` `print``(findDiff(str1, str2)) ` ` `  `# This code is contributed by avanitrachhadiya2155`

## C#

 `// C# program to find difference of ` `// two large numbers. ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// Returns true if str1 is smaller ` `    ``// than str2, else false. ` `    ``static` `bool` `isSmaller(``string` `str1, ``string` `str2) ` `    ``{ ` `        ``// Calculate lengths of both string ` `        ``int` `n1 = str1.Length, n2 = str2.Length; ` ` `  `        ``if` `(n1 < n2) ` `            ``return` `true``; ` `        ``if` `(n2 < n1) ` `            ``return` `false``; ` ` `  `        ``for` `(``int` `i = 0; i < n1; i++) { ` `            ``if` `(str1[i] < str2[i]) ` `                ``return` `true``; ` `            ``else` `if` `(str1[i] > str2[i]) ` `                ``return` `false``; ` `        ``} ` `        ``return` `false``; ` `    ``} ` ` `  `    ``// Function for finding difference of ` `    ``// larger numbers ` `    ``static` `string` `findDiff(``string` `str1, ``string` `str2) ` `    ``{ ` `        ``// Before proceeding further, ` `        ``// make sure str1 is not smaller ` `        ``if` `(isSmaller(str1, str2)) { ` `            ``string` `t = str1; ` `            ``str1 = str2; ` `            ``str2 = t; ` `        ``} ` ` `  `        ``// Take an empty string for ` `        ``// storing result ` `        ``String str = ``""``; ` ` `  `        ``// Calculate lengths of both string ` `        ``int` `n1 = str1.Length, n2 = str2.Length; ` `        ``int` `diff = n1 - n2; ` ` `  `        ``// Initially take carry zero ` `        ``int` `carry = 0; ` ` `  `        ``// Traverse from end of both strings ` `        ``for` `(``int` `i = n2 - 1; i >= 0; i--) { ` `            ``// Do school mathematics, compute ` `            ``// difference of current digits and carry ` `            ``int` `sub = (((``int``)str1[i + diff] - (``int``)``'0'``) ` `                       ``- ((``int``)str2[i] - (``int``)``'0'``) - carry); ` `            ``if` `(sub < 0) { ` `                ``sub = sub + 10; ` `                ``carry = 1; ` `            ``} ` `            ``else` `                ``carry = 0; ` ` `  `            ``str += sub.ToString(); ` `        ``} ` ` `  `        ``// subtract remaining digits of str1[] ` `        ``for` `(``int` `i = n1 - n2 - 1; i >= 0; i--) { ` `            ``if` `(str1[i] == ``'0'` `&& carry > 0) { ` `                ``str += ``"9"``; ` `                ``continue``; ` `            ``} ` `            ``int` `sub = (((``int``)str1[i] - (``int``)``'0'``) - carry); ` `            ``if` `(i > 0 || sub > 0) ``// remove preceding 0's ` `                ``str += sub.ToString(); ` `            ``carry = 0; ` `        ``} ` ` `  `        ``// reverse resultant string ` `        ``char``[] aa = str.ToCharArray(); ` `        ``Array.Reverse(aa); ` `        ``return` `new` `string``(aa); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``String str1 = ``"88"``; ` `        ``String str2 = ``"1079"``; ` ` `  `        ``// Function call ` `        ``Console.WriteLine(findDiff(str1, str2)); ` `    ``} ` `} ` ` `  `// This code is contributed by mits`

## PHP

 ` ``\$str2``[``\$i``]) ` `            ``return` `false; ` `    ``} ` `    ``return` `false; ` `} ` ` `  `// Function for finding difference  ` `// of larger numbers ` `function` `findDiff(``\$str1``, ``\$str2``) ` `{ ` `    ``// Before proceeding further, make  ` `    ``// sure str1 is not smaller ` `    ``if` `(isSmaller(``\$str1``, ``\$str2``)) ` `    ``{ ` `        ``\$t` `= ``\$str1``; ` `        ``\$str1` `= ``\$str2``; ` `        ``\$str2` `= ``\$t``; ` `    ``} ` ` `  `    ``// Take an empty string for storing result ` `    ``\$str` `= ``""``; ` ` `  `    ``// Calculate lengths of both string ` `    ``\$n1` `= ``strlen``(``\$str1``);  ` `    ``\$n2` `= ``strlen``(``\$str2``); ` `    ``\$diff` `= ``\$n1` `- ``\$n2``; ` ` `  `    ``// Initially take carry zero ` `    ``\$carry` `= 0; ` ` `  `    ``// Traverse from end of both strings ` `    ``for` `(``\$i` `= ``\$n2` `- 1; ``\$i` `>= 0; ``\$i``--) ` `    ``{ ` `        ``// Do school mathematics, compute  ` `        ``// difference of current digits and carry ` `        ``\$sub` `= ((ord(``\$str1``[``\$i` `+ ``\$diff``]) - ord(``'0'``)) -  ` `                ``(ord(``\$str2``[``\$i``]) - ord(``'0'``)) - ``\$carry``); ` `        ``if` `(``\$sub` `< 0) ` `        ``{ ` `            ``\$sub` `= ``\$sub` `+ 10; ` `            ``\$carry` `= 1; ` `        ``} ` `        ``else` `            ``\$carry` `= 0; ` ` `  `        ``\$str``.=``chr``(``\$sub` `+ ord(``"0"``)); ` `    ``} ` ` `  `    ``// subtract remaining digits of str1[] ` `    ``for` `(``\$i` `= ``\$n1` `- ``\$n2` `- 1; ``\$i` `>= 0; ``\$i``--) ` `    ``{ ` `        ``if` `(``\$str1``[``\$i``] == ``'0'` `&& ``\$carry` `> 0) ` `        ``{ ` `            ``\$str``.=``"9"``; ` `            ``continue``; ` `        ``} ` `        ``\$sub` `= (ord(``\$str1``[``\$i``]) - ord(``'0'``) - ``\$carry``); ` `        ``if` `(``\$i` `> 0 || ``\$sub` `> 0) ``// remove preceding 0's ` `            ``\$str``.=``chr``(``\$sub` `+ ord(``"0"``)); ` `        ``\$carry` `= 0; ` ` `  `    ``} ` ` `  `    ``// reverse resultant string ` `    ``return` `strrev``(``\$str``); ` ` `  `} ` ` `  `// Driver code ` `\$str1` `= ``"88"``; ` `\$str2` `= ``"1079"``; ` ` `  `// Function call ` `print``(findDiff(``\$str1``, ``\$str2``)); ` ` `  `// This code is contributed by chandan_jnu ` `?> `

## Javascript

 ``

Output

`991`

Time complexity : O(n1 + n2)

Auxiliary Space: O(max(n1, n2))

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